Kardar-Parisi-Zhang growth on one-dimensional decreasing substrates

Area of Science:

• Complex Systems
• Statistical Physics
• Nonlinear Dynamics

Background:

• Conflicting experimental results exist for one-dimensional (1D) circular Kardar-Parisi-Zhang (KPZ) systems with decreasing radii.
• Understanding interface dynamics in systems with time-varying sizes is crucial.

Purpose of the Study:

• To investigate 1D KPZ models on substrates with time-dependent sizes (L(t)=L_{0}+ωt), focusing on shrinking systems (ω<0).
• To clarify the transient and asymptotic interface statistics in these dynamic systems.

Main Methods:

• Extensive numerical simulations of 1D KPZ models.
• Analysis of interface statistics under varying substrate sizes and growth conditions.
• Generalization of Family-Vicsek scaling for ingrowing interfaces.

Main Results:

• A transient regime exhibiting flat KPZ statistics (ω=0 case) is observed for large initial sizes (L_{0}≫1), irrespective of whether the system is ingrowing (ω<0) or outgrowing (ω>0).
• Divergence between ingrowing and outgrowing systems occurs at long times (t∼L_{0}/|ω|), with outgrowing systems showing curved statistics and ingrowing systems becoming fully correlated.
• A generalized Family-Vicsek scaling for ingrowing interfaces is presented.

Conclusions:

• Transient flat statistics is a general characteristic of KPZ systems starting with large sizes, regardless of curvature.
• Observed discrepancies in experimental results (e.g., turbulent liquid crystals vs. colloidal deposition) may be explained by system size, transient behavior, and analysis duration.
• The study provides a unified framework for understanding interface dynamics in time-varying KPZ systems.